EE 5340 Semiconductor Device Theory Lecture 28 - Fall 2003 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc L 28 Dec 02

n-channel enhancement MOSFET in ohmic region 0< VT< VG Channel VS = 0 0< VD< VDS,sat EOx,x> 0 n+ e-e- e- e- e- n+ Depl Reg p-substrate Acceptors VB < 0 L 28 Dec 02

Fully biased n- channel VT calc L 28 Dec 02

Fully biased p- channel VT calc L 28 Dec 02

“Dotted box” approx** L 28 Dec 02

Calculating xi and DVT L 28 Dec 02

MOS energy bands at Si surface for n-channel Fig 8.10** L 28 Dec 02

If xi << xd,max calc. VT from effective DQ’ss Fig 8.11** |Q’d,max|/q (cm-2) xd,max (microns) L 28 Dec 02

Flat band with oxide charge (approx. scale) SiO2 p-Si +<--Vox-->- q(Vox) Ec,Ox q(ffp-cox) q(fm-cox) Ex Eg,ox~8eV EFm Ec EFi EFp q(VFB) Ev VFB= VG-VB, when Si bands are flat Ev L 28 Dec 02

Fully biased n- channel VT calc L 28 Dec 02

If xi ~ xd,max L 28 Dec 02

Calculating VT L 28 Dec 02

Implanted VT Vt per Eq. 9.1.23 in M&K for a MOSFET with an 87-nm-thick gate oxide, Qff/q = 1011 cm-2, N’ = 3.5 X 1011 cm-2, and Na = 2 X 1015 cm-3. Both VS and VB = Figure 9.8 (p. 441) L 28 Dec 02

Mobilities** L 28 Dec 02

M&K Fig. 9.9 (Eq. 9.1.23) L 28 Dec 02

Mobilities** L 28 Dec 02

Subthreshold conduction Below O.S.I., when the total band-bending < 2|fp|, the weakly inverted channel conducts by diffusion like a BJT. Since VGS>VDS, and below OSI, then Na>nS >nD, and electr diffuse S --> D Electron concentration at Source Concentration gradient driving diffusion L 28 Dec 02

M&K Fig.9.10 (p.443) Band diagram along the channel region of an n-channel MOSFET under bias, indicating that the barrier qΦB at the source depends on the gate voltage. L 28 Dec 02

M&K Fig. 9.11 (p.444) Measured subthreshold characteristics of an MOS transistor with a 1.2 μm channel length. The inverse slope of the straight-line portion of this semilogarithmic plot is called the drain-current subthreshold slope S (measured in mV/decade of drain current). L 28 Dec 02

Subthreshold current data Figure 10.1** Figure 11.4* L 28 Dec 02

Mobility variation due to Edepl Figures 11.7,8,9* L 28 Dec 02

Velocity saturation effects Figure 11.10* L 28 Dec 02

Final Exam For BOTH sections, 051 and 001 The Final is comprehensive 8:00 to 10:30 AM Tuesday, December 9 in 206 ACT Cover sheet on web page at http://www.uta.edu/ronc/5340/tests/ The Final is comprehensive 20% to 25% on Test 1 material 20% to 25% on Test 2 material Balance of final on material since Test 2 L 28 Dec 02

References * Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997. **Device Electronics for Integrated Circuits, 2nd ed., by Richard S. Muller and Theodore I. Kamins, John Wiley and Sons, New York, 1986 L 28 Dec 02